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myininaya Group Title

I have the following information: \[n=p^2q\] \[k \ge 4\] \[0<v<n\] \[0 \le x < pq\] \[y=\lceil \frac{(v-x^k) \mod n}{pq} \rceil \cdot (kx^{k-1})^{-1} \mod p\] I want to show: \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k-1}(ypq)^i \equiv x^k+kypqx^{k-1}\] the congruence is mod n

  • 3 years ago
  • 3 years ago

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  1. satellite73 Group Title
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    i can't even read this what class?

    • 3 years ago
  2. myininaya Group Title
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    i made a mistake \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k-i}(ypq)^i \equiv x^k+kypqx^{k-1}\] I'm trying to follow a proof but i don't know how they got from that one part to the other part

    • 3 years ago
  3. satellite73 Group Title
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    yeah well i cannot read what it says. good luck

    • 3 years ago
  4. myininaya Group Title
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    http://www.cacr.math.uwaterloo.ca/hac/ its in chapter 11 on page 473 at the bottom

    • 3 years ago
  5. myininaya Group Title
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    ;p;

    • 3 years ago
  6. myininaya Group Title
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    lol*

    • 3 years ago
  7. myininaya Group Title
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    i wonder if james or zarkon could do it

    • 3 years ago
  8. myininaya Group Title
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    oh its zarkon lol

    • 3 years ago
  9. satellite73 Group Title
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    good luck!

    • 3 years ago
  10. KingGeorge Group Title
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    ask me next semester when I've taken cryptography, and I might be able to help you, but right now, I haven't got a clue.

    • 3 years ago
  11. Zarkon Group Title
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    only the first two values of i will matter (i=0,1) for i>1 you have a \((pq)^2\) part which is \(p^2qq=nq\) which is zero nod n

    • 3 years ago
  12. myininaya Group Title
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    i don't see this (pq)^2 part

    • 3 years ago
  13. myininaya Group Title
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    george what kind of math have you had?

    • 3 years ago
  14. Zarkon Group Title
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    \[{k\choose i}x^{k-1}(ypq)^i\] for \(i\ge2\) \[{k\choose i}x^{k-1}(ypq)^i={k\choose i}x^{k-1}(y^i)(pq)^{i-2}p^2qq\] \[=\left({k\choose i}x^{k-1}(y^i)(pq)^{i-2}q\right)\times n\]

    • 3 years ago
  15. myininaya Group Title
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    ok i see

    • 3 years ago
  16. myininaya Group Title
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    you are so smart to notice the first two values will only matter since n mod n is like totally 0 thanks zarkon

    • 3 years ago
  17. KingGeorge Group Title
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    I've only had a year and a half of college level math so far, so that means, calc 1-3, lin. algebra, abstract algebra, and analysis

    • 3 years ago
  18. Zarkon Group Title
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    no problem :)

    • 3 years ago
  19. myininaya Group Title
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    is there any number theory in abstract algebra i can't remember

    • 3 years ago
  20. KingGeorge Group Title
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    not very much. I'm taking intro to number theory, and cryptography next semester.

    • 3 years ago
  21. myininaya Group Title
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    i like cryptography

    • 3 years ago
  22. myininaya Group Title
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    number theory is so cool and interesting to me although my skills suck right now

    • 3 years ago
  23. KingGeorge Group Title
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    It certainly sounds fun. I'm definitely enjoying my abstract algebra class right now. We had the barest hints of some number theory in discrete math so I'm not completely helpless.

    • 3 years ago
  24. myininaya Group Title
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    i like these math puzzles

    • 3 years ago
  25. myininaya Group Title
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    differential equations is not as fun to me but i do like the remedial kind lol

    • 3 years ago
  26. myininaya Group Title
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    zarkon do you think there is hope for my brain?

    • 3 years ago
  27. KingGeorge Group Title
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    From my experience, I don't like differential equations very much. Granted, I've never had a full course in it, but it just isn't my thing.

    • 3 years ago
  28. Zarkon Group Title
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    there is!

    • 3 years ago
  29. myininaya Group Title
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    i feel like i'm trapped inside with an apes' brain

    • 3 years ago
  30. Zarkon Group Title
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    A very smart ape ;)

    • 3 years ago
  31. myininaya Group Title
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    thanks i take that as a compliment

    • 3 years ago
  32. Zarkon Group Title
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    If you want a fun class...Take a course in measure theoretic probability theory.

    • 3 years ago
  33. myininaya Group Title
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    he says that because he is a stat nerd

    • 3 years ago
  34. KingGeorge Group Title
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    I don't think my school has that class...

    • 3 years ago
  35. myininaya Group Title
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    my doesn't either

    • 3 years ago
  36. Zarkon Group Title
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    or a class in stochastic processes

    • 3 years ago
  37. Zarkon Group Title
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    sometimes it will fall under the title of applied probability

    • 3 years ago
  38. myininaya Group Title
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    i think they might have that

    • 3 years ago
  39. myininaya Group Title
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    i always had a 10 foot pole when it came to statistics i only had to put it down when the course in stat was required

    • 3 years ago
  40. KingGeorge Group Title
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    I'm personally more of an algebra person. Stats was interesting at first, but then it got boring.

    • 3 years ago
  41. myininaya Group Title
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    There are some cool things though in stat i do admit

    • 3 years ago
  42. Zarkon Group Title
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    There is plenty of really nice mathematics in statistics

    • 3 years ago
  43. KingGeorge Group Title
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    It was the same with calculus for me. Interesting at first, and then it just stopped interesting me.

    • 3 years ago
  44. Zarkon Group Title
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    A lot of multivariate calculus and matrix theory

    • 3 years ago
  45. myininaya Group Title
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    zarkon can i ask another question

    • 3 years ago
  46. myininaya Group Title
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    this is my last problem with this proof...

    • 3 years ago
  47. Zarkon Group Title
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    ok

    • 3 years ago
  48. myininaya Group Title
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    omg never i got it lol

    • 3 years ago
  49. myininaya Group Title
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    i mean nvm

    • 3 years ago
  50. myininaya Group Title
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    i was typing it all out then i realized oh yeah lol

    • 3 years ago
  51. Zarkon Group Title
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    ok :)

    • 3 years ago
  52. myininaya Group Title
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    ok i feel good about this proof thanks for all your help

    • 3 years ago
  53. Zarkon Group Title
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    good...no problem

    • 3 years ago
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